Coupling free and porous-media flows: models and numerical approximation

In this paper we provide an overview of mathematical and numerical models for the coupling of the Navier-Stokes and the Darcy equations to describe the filtration of incompressible flows through porous media. After introducing suitable interface conditions, we set up the coupled problem and, using domain decomposition techniques, we present possible algorithms to compute its finite element approximation through the independent solution of the Navier-Stokes and of the Darcy equations in their respective subdomains. Keywords. Navier-Stokes equations, Darcy’s law, interface conditions, domain decomposition, finite elements method